P,T-invariant system of Chern-Simons fields: Pseudoclassical model and hidden symmetries

TL;DR

This paper explores hidden symmetries in a P,T-invariant topologically massive gauge field system, introducing a pseudoclassical model that reveals U(1,1) and S(2,1) supersymmetries at the quantum level.

Contribution

It proposes a pseudoclassical model for P,T-invariant Chern-Simons fields that uncovers nontrivial hidden symmetries and their covariant representations.

Findings

Identification of U(1,1) symmetry as a hidden symmetry.

Discovery of S(2,1) supersymmetry in the quantum system.

Representation of states as irreducible super-extensions of the Poincare group.

Abstract

We investigate hidden symmetries of P,T-invariant system of topologically massive U(1) gauge fields. For this purpose, we propose a pseudoclassical model giving rise to this field system at the quantum level. The model contains a parameter, which displays a quantization property at the classical and the quantum levels and demonstrates a nontrivial relationship between continuous and discrete symmetries. Analyzing the integrals of motion of the pseudoclassical model, we identify U(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. Representing the hidden symmetries in a covariant form, we show that one-particle states realize an irreducible representation of a non-standard super-extension of the (2+1)-dimensional Poincare group labelled by the zero eigenvalue of the superspin.